ABSTRACT
This chapter focuses on methods for single specific contrasts, in most actual studies more than one contrast will usually be of interest. It presents the rationale for formulas for testing individual comparisons. Several comparisons are indeed tested, leading to the topic of multiple comparisons. The desire to test multiple comparisons can arise in either of two circumstances. First, there are occasions in which a researcher may decide to test several specific comparisons either instead of or in addition to performing a test of the omnibus null hypothesis that all population means are equal. Second, on other occasions, the omnibus null hypothesis is tested. If it is rejected, further data analyses are conducted to explore which groups contributed to the statistically significant result. Although some research questions center on pairwise comparisons, other hypotheses may concern a difference involving more than two means. The problem of testing mean differences when variances are unequal has plagued statisticians for several decades.
